Analysis of contributors to Prosper loan scores
by Charles Dellinger
The data set is about personal loans made through Prosper Marketplace. Prosper anonymously connects private users who want to lend and borrow money. The marketplace allows users to apply and receive loans from $2,000 to $40,000. During the application process, fairly standard information, like income, occupation, assets, and credit score, is collected. The application information with additional data about the loan itself, including current state, is what this data set contains. A full list of data collected about each loan is below:
## [1] "AmountDelinquent"
## [2] "AvailableBankcardCredit"
## [3] "BankcardUtilization"
## [4] "BorrowerAPR"
## [5] "BorrowerRate"
## [6] "BorrowerState"
## [7] "ClosedDate"
## [8] "CreditGrade"
## [9] "CreditScoreRangeLower"
## [10] "CreditScoreRangeUpper"
## [11] "CurrentCreditLines"
## [12] "CurrentDelinquencies"
## [13] "CurrentlyInGroup"
## [14] "DateCreditPulled"
## [15] "DebtToIncomeRatio"
## [16] "DelinquenciesLast7Years"
## [17] "EmploymentStatus"
## [18] "EmploymentStatusDuration"
## [19] "EstimatedEffectiveYield"
## [20] "EstimatedLoss"
## [21] "EstimatedReturn"
## [22] "FirstRecordedCreditLine"
## [23] "GroupKey"
## [24] "IncomeRange"
## [25] "IncomeVerifiable"
## [26] "InquiriesLast6Months"
## [27] "InvestmentFromFriendsAmount"
## [28] "InvestmentFromFriendsCount"
## [29] "Investors"
## [30] "IsBorrowerHomeowner"
## [31] "LenderYield"
## [32] "ListingCategory..numeric."
## [33] "ListingCreationDate"
## [34] "ListingKey"
## [35] "ListingNumber"
## [36] "LoanCurrentDaysDelinquent"
## [37] "LoanFirstDefaultedCycleNumber"
## [38] "LoanKey"
## [39] "LoanMonthsSinceOrigination"
## [40] "LoanNumber"
## [41] "LoanOriginalAmount"
## [42] "LoanOriginationDate"
## [43] "LoanOriginationQuarter"
## [44] "LoanStatus"
## [45] "LP_CollectionFees"
## [46] "LP_CustomerPayments"
## [47] "LP_CustomerPrincipalPayments"
## [48] "LP_GrossPrincipalLoss"
## [49] "LP_InterestandFees"
## [50] "LP_NetPrincipalLoss"
## [51] "LP_NonPrincipalRecoverypayments"
## [52] "LP_ServiceFees"
## [53] "MemberKey"
## [54] "MonthlyLoanPayment"
## [55] "Occupation"
## [56] "OnTimeProsperPayments"
## [57] "OpenCreditLines"
## [58] "OpenRevolvingAccounts"
## [59] "OpenRevolvingMonthlyPayment"
## [60] "PercentFunded"
## [61] "ProsperPaymentsLessThanOneMonthLate"
## [62] "ProsperPaymentsOneMonthPlusLate"
## [63] "ProsperPrincipalBorrowed"
## [64] "ProsperPrincipalOutstanding"
## [65] "ProsperRating..Alpha."
## [66] "ProsperRating..numeric."
## [67] "ProsperScore"
## [68] "PublicRecordsLast10Years"
## [69] "PublicRecordsLast12Months"
## [70] "Recommendations"
## [71] "RevolvingCreditBalance"
## [72] "ScorexChangeAtTimeOfListing"
## [73] "StatedMonthlyIncome"
## [74] "Term"
## [75] "TotalCreditLinespast7years"
## [76] "TotalInquiries"
## [77] "TotalProsperLoans"
## [78] "TotalProsperPaymentsBilled"
## [79] "TotalTrades"
## [80] "TradesNeverDelinquent..percentage."
## [81] "TradesOpenedLast6Months"Univariate Exploration
Univariate Plots Section
IncomeRange
The histogram of IncomeRange shows that most of the borrowers make between $25,000 to $75,000. However, there’s a decent amount of ‘Not displayed’, which is assumed to be borrower’s who wanted to abstain from reporting or having it reported. The ‘Not displayed’ seems to be a lot smaller than most of the range counts, so it isn’t likely to cause a misrepresentation if this variable is used.
StatedMonthlyIncome
The stated monthly incomes look to be all bunched up in the low end. Zooming in on the plot will give a better idea of the distribution.
The stated monthly income histogram paints a slightly different picture than the income range bins. The income range bins had more of a bell-curve type shape, whereas the stated income curve looks skewed right.
Will the StatedMonthlyIncome look the same if it is sorted into buckets?
The histogram of StatedMonthlyIncome buckets doesn’t seem to align with the income buckets outlined by IncomeRange. Since most of the incomes are all in one range, there’s some problem with the StatedMonthlyIncome variable.
Occupation
Occupation is going to be pretty useless for categorization as it is since there are so many. Even if grouped, a category like healthcare workers would have different results for instance with a “Nurse’s Aide” versus a “Doctor”. Also, the catch-all’s of “Other” and “Professional” are ambiguous and seem to dominate; the proportion of Occupation entries:
## Professional Other Everything Else
## 0.1196100 0.2511651 0.6292249With almost 40% of Occupation entries unusable, the subgroup analysis probably won’t produce generalizable results.
Debt-to-Income Ratio
Almost all the debt-to-income ratios are less than 1. People with more debt to pay than their income would have an almost 100% chance of default.
## <= 1 > 1
## 104584 799Creating custom bins can help get a better feel with for the data with smaller bins in the lower ratio sections to see finer details there.
Delinquencies in the Last 7 Years
The users applying for loans had a fair number of instances where the payments were late. This metric is a mixed bag for lenders as it would mean that the borrower would accrue interest but also the borrower has a higher risk of default.
Total Trades on the Prosper Platform
In general, the number of trades is skewed to the right, but the curve between 0 and 50 shows that a lot of borrowers are repeat users.
Term Length of Loans
The loans seem to be grouped in three discrete lengths.
| Term | N |
|---|---|
| 12 | 1614 |
| 36 | 87778 |
| 60 | 24545 |
The table confirms that the data set contains only three loan lengths, which correspond to 1, 3, and 5 years. This variable would be a good variable to change to a categorical variable to split other plots in the future.
Home Ownership
Home ownership would show that a person has an asset, which would make the loan more viable because the borrower can both make payments and has something to borrow against if they need money to meet their liabilities.
This variable might be a good one to use to see split scores or behavior between those that own a home or not.
BankcardUtilization
This variable is strange: “The percentage of available revolving credit that is utilized at the time the credit profile was pulled.” It seems like the amount of available credit that the borrower is utilizing, or home much of the credit card potential have they used.
| Statistic | Value |
|---|---|
| Min. | 0.00 |
| 1st Qu. | 0.31 |
| Median | 0.60 |
| Mean | 0.56 |
| 3rd Qu. | 0.84 |
| Max. | 5.95 |
| NA’s | 7604.00 |
The shape of the bank card utilization histogram shows a spike at 0% and then an increasing trend as the percentage approaches 100%. The box plot show that there are a fair number of people that have somehow over-drafted their bank cards to a pretty high extent. The bank card percentage score would be an interesting metric to test correlations to in the multivariate analysis.
Credit Score Range
The shapes of the upper and lower credit scores histograms look roughly the same, so I would expect that the ranges are of a standard length of points. A quick graph of the differences will confirm.
##
## 19
## 113346Since the scores are of fixed length, any use of credit scores can use either one to view any trends or make predictions.
Prosper Score
##
## 1 2 3 4 5 6 7 8 9 10 11
## 992 5766 7642 12595 9813 12278 10597 12053 6911 4750 1456There seem to be only discrete Prosper scores and for some reason there are score at 11, despite the range in the variable definition file indicating the maximum is 10. Since Prosper score is made up of discrete levels, it can be transformed into a categorical variable.
Borrower APR
The peak for borrower rates is on par with credit card rates with a roughly even distribution above and below. This variable will probably be good to use as a predictor.
Loan Amount
According to the Prosper website, the loans are from $2000 to $40000. Most of the loans are of low value, but there are some clear spikes at higher numbers at 5k intervals ($10000, $15000, $20000, $25000), which shows a bias for people rounding off for their needs.
Univariate Analysis
What is the structure of your dataset?
There are 113937 entries, each containing 84 variables of different types.
All of the data categories are related to whether the loan would be a good investment or not, which is presumably wrapped into their proprietary Prosper score.
What is/are the main feature(s) of interest in your dataset?
The main features of concern are going to be the variables that are commonly primary contributors to risk, such as assets, liabilities, and current state of leverage. Presumably these will be rolled up and reflected in the Prosper score (“ProsperScore”). The following are a listing of those variables: “IncomeRange”, “DebtToIncomeRatio”, “DelinquenciesLast7Years”, “TotalTrades”, “Term”, “IsBorrowerHomeowner”, “BankcardUtilization”, “BorrowerAPR”, “LoanOriginalAmount”, “CreditScoreRangeLower”/“CreditScoreRangeUpper”
What other features in the dataset do you think will help support your
investigation into your feature(s) of interest?
Additional features that might build a richer picture would include: “ListingCategory..numeric.” - to see what the loan is for “LoanStatus” - to check on overdue loans “Investors” - how many people have confidence that the borrower will pay? “Recommentations” - how many people vouch for the borrower? “EmploymentStatusDuration” - is the borrower’s cash flow consistent? “Estimated Return” - to measure risk/benefit ratio “Estimated Loss” - complement of the return
Did you create any new variables from existing variables in the dataset?
I created IncomeRange2 and StatedMonthlyIncome.bucket: * IncomeRange2 - consolidates “Not employed” to have an income of $0 * StatedMonthlyIncome.bucket - bucketed the StatedMonthlyIncome to test against IncomeRange, but the results made it seem like the monthly income wasn’t as reliable. * Term2 - changed Term into a categorical variable * ProsperScore2 - changed ProsperScore into a categorical variable
Of the features you investigated, were there any unusual distributions?
Did you perform any operations on the data to tidy, adjust, or change the form
of the data? If so, why did you do this?
All the data were skewed appropriately or of a normalized scoring. The exceptions to a lot of distributions were around even number intervals, because people round their expectation needs.
There were some strange things within some of the variables. The Prosper score had scores of 11 even though the range was stated to be 1-10. There were bankcard utilizations and debt-to-income ratios that were questionable, because the borrower had much greater debt than they could pay, like the borrower that had almost 600% bankcard utilization and the 799 borrowers that had more debt payments per month than their monthly income.
Bivariate & Multivariate Exploration
In general, the bivariate plots didn’t show anything unless augmented by another variable, so the plot sections have been merged together. Most of the plots are multivariate, but there are a few bivariate where the relationship is straightforward enough.
Bivariate & Multivariate Plots Section
A quick grid of relationships to see if anything sticks out:
Prosper score seems like a good place to start looking at affects of variables on each other since it is a sort of summation of risk for the loan. The amount of risk is usually passed on as a loan penalty in the form of APR. Therefore, there should be relationship between Prosper and APR such that increased Prosper score should have a lower APR and vice versa.
As expected, there’s a relationship with borrower APR and Prosper score. The higher the Prosper score, the less risk, so the APR is lower. The coloring of the visualization doesn’t reveal that Term clearly augments this relationship despite longer term loans having an intrinsically higher risk.
Since Prosper score is proprietary, it will be interesting to find out what else goes into the Proper score. Outside of Prosper, APRs generally trend with the non-proprietary credit score, so Prosper score and credit score would be expected to be roughly trend together.
Strangely, there doesn’t seem to be much correlation if any between Prosper score and Credit score despite both being compilation measures of risk for financial institutions. Just how weak is the correlation?
##
## Pearson's product-moment correlation
##
## data: ProsperScore and CreditScoreRangeLower
## t = 115.87, df = 84851, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.3637793 0.3753979
## sample estimates:
## cor
## 0.369603Despite the weak correlation of Prosper score and credit score, the coloring of the visualization does reveal that people with higher income are more likely to have a higher Prosper score, regardless of credit score.
##
## Pearson's product-moment correlation
##
## data: ProsperScore and BorrowerAPR
## t = -261.68, df = 84851, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.6719940 -0.6645469
## sample estimates:
## cor
## -0.6682872##
## Pearson's product-moment correlation
##
## data: CreditScoreRangeLower and BorrowerAPR
## t = -160.21, df = 113340, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4344422 -0.4249487
## sample estimates:
## cor
## -0.4297073Another measure of interest would be the relationship between the debt-to-income ratio and Prosper score, since it is more risky to grant a loan to a borrower as their amount of existing debt increases, or the borrower is more leveraged.
The relationship between debt-to-income ratio and Prosper score isn’t as obvious as expected, but the debt-to-income ratio range for the Prosper score extends farther into a bad ratio for lower Prosper scores. However, the visualization does show a relationship between the Prosper scare and income range. Borrowers with a higher income are more likely to have a higher Prosper score across all debt-to-income ratios.
Does total trades affect the Prosper score?
The total number of trades on the platform doesn’t affect the Prosper score. To eliminate the possibility of delinquent trades and good trades mixed together causing hiding any trend, coloring based on percentage of good trades was added. The coloring shows that all the colors are dispersed fairly evenly, so there really isn’t any trend.
The amount of delinquencies should affect the BorrowerAPR and Prosper score, since delinquencies could be a sign that the borrow has a hard time paying back the loan.
The expected trend between APR and delinquencies doesn’t seem to show up even when coloring based on previously identified categories. Will Prosper score show the same lack of trend? Or will the expected trend appear?
Another logical affector on measures of risk (Prosper score and borrower APR) would be how much available credit a borrower has to fulfill the obligation to the Prosper loan. In theory, its a liquidity measure, so the more unused immediately usable credit, the higher the Prosper score and lower the APR.
The expected trends hold up for Prosper score and APR vs bankcard utilization.
There haven’t been too many trends in the Prosper score, so borrower APR will be the focus moving forward.
Looking at the income range and borrower APR visualization, the APR’s of higher income borrowers are consolidated in a narrower areas in the lower APR range. The high income borrowers look more likely to take out loans of higher amounts. Lower income borrowers with low APR seem slightly more likely to take out larger loan amounts.
